LaserZone was another psychadelic blaster from Jeff Minter.
It was one of my favourite games on the C64 (all LlamaSoft games were great).

An accident with a time machine and some DNA manipulating nanobots has created mutant strains of creatures throughout the ages of history.
Your job is to clean sufficient numbers of these mutants from each period to prevent them from taking over.
Two time points in each period will have to be cleared to fully clear that period.
To achieve this a pair of laser turrets has been projected through time to near where the mutants are located. The turrets can only move a limited distance, but the mutants will be attracted by the temporal distortion and should come running towards you as fast as possible.
Once sufficent mutants have been cleared from a period you will proceed to the next time period.